Genomic DNA is always present with a ton of other biomolecules within a cell. Extracting pure DNA from the typical cellular mix of DNA, RNA, proteins, carbohydrates, lipids, etc. isn't much of a challenge anymore using modern molecular biology, but it is still necessary to study specific genes.

The DNA for a specific naturally occuring gene is only a tiny portion of the total DNA extracted from a cell.

Since 1990 or so, purification of this (relatively) small piece of DNA for a particular gene (from the enormous quantity of genomic DNA) has become pretty trivial in most cases. This is largely due to the invention of the Polymerase Chain Reaction [http://en.wikipedia.org/wiki/PCR] and the maturation of gene cloning techniques.